Scientific and pedagogical staff

Yampolskyi Oleksandr Leonidovych

Doctor of Physical and Mathematical Sciences in the specialty «Geometry and Topology», Professor at the Department of Fundamental Mathematics

  • 2021: Awarded academic title: Professor at the Department of Fundamental Mathematics.
  • 2015: Obtained scientific degree: Doctor of Physical and Mathematical Sciences. Dissertation: «Geometry of Submanifolds in Fibered Spaces».
  • 1991: Awarded academic title: Associate Professor at the Department of Geometry.
  • 1986: Awarded the academic degree of Candidate of Physical and Mathematical Sciences, Odessa State University (Ukraine). Dissertation: “On the Sasaki Metric of Tangent and Normal Stratifications.”
  • 1982 – 1986: Postgraduate student of the Faculty of Mechanics and Mathematics of Kharkiv National University, Kharkiv, Ukraine.
  • 1978: Earned a Master’s degree in Mathematics (equivalent), Kharkiv National University.
  • 1973–1978: Student at the Faculty of Mechanics and Mathematics, Kharkiv National University, Kharkiv.

Total length of service in teaching positions: 40 years

2022–present: Professor, Department of Fundamental Mathematics, School of Mathematics and Computer Science, V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

2023: Instructor for the MATH 119 course “Mathematical Analysis 2,” University of Waterloo, Waterloo, Ontario, Canada.

2022–2023: Visiting Researcher in the Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada.

2016–2022: Chair of the Department of Fundamental Mathematics, School of Mathematics and Computer Science, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine.

2014–2015: Chair of the Department of Geometry, Faculty of Mechanics and Mathematics, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine.

2021: Professor in the Department of Fundamental Mathematics, School of Mathematics and Computer Science, Kharkiv National University, Kharkiv, Ukraine.

2015: Doctor of Physical and Mathematical Sciences. Dissertation: “The Geometry of Subvarieties in Layered Spaces.” Faculty of Theoretical Physics and Mathematics, National Academy of Sciences of Ukraine.

1991: Associate Professor in the Department of Geometry.

1986–1986: Assistant in the Department of Geometry, Faculty of Mechanics and Mathematics, Kharkiv National University, Kharkiv, Ukraine.

1986: Candidate of Physical and Mathematical Sciences, Odessa State University (Ukraine). Dissertation: “On the Sasaki Metric of Tangent and Normal Stratifications.”

1982–1986: Graduate student in the Department of Geometry, Kharkiv National University, Kharkiv, Ukraine.

1973–1978: Studied at the Faculty of Mechanics and Mathematics, Kharkiv National University, Kharkiv, Ukraine.

  • Differential geometry
  • Riemannian geometry
  • Delamination
  • Applications of Computer Mathematics

Links to pages on academic networks:

Lecture courses for bachelor's students

  • Analytical Geometry: 9 credits (270 hours)
  • Differential Geometry: 8 credits (240 hours)
  • Classical Problems in Geometry “in General”: 4 credits (120 hours)
  • Symbolic Computation and Modeling: 5 credits (150 hours)
  • Practical Exercises in Analytic and Differential Geometry

Lecture courses for master's students:

  • Geometry of Layered Spaces: 4 credits (120 hours)
  • Fundamentals of Scientific Research: 3 credits (90 hours)

Lecture courses for postgraduate students:

  • Modern methods of obtaining and presenting research results in mathematics: 5 credits (150 hours)

Supervision of postgraduate students:

  • Lotarets L.A. (defense 2025)
  • Shuhailo O.O. (defended, 2015)
  1. Yampolsky A.  Minimal unit vector fields on oscillator groups. Book series “Springer Proceedings in Mathematics & Statistics”, “Differential Geometric Structures and Applications”. 4th International Workshop on Differential Geometry, Haifa, Israel, May 10 – 13, 2023, Haifa, Israel. P. 117-133. https://doi.org/10.1007/978-3-031-50586-7
  2. Yampolsky A.  On properties of the Reeb vector field of trans-Sasakian structure. Turkish Journal of Mathematics, 2022, Vol. 46: No. 6, Article 19. https://doi.org/10.55730/1300-0098.3271
  3. Yampolsky A.  On Projective Classification of Points of a Submanifold in the Euclidean Space. Journal of Mathematical Physics, Analysis, Geometry. 2020. V. 16, № 3, P. 364–371.
  4. Yampolsky A. Catacaustics of a hypersurface in the Euclidean n-space. Mediterranean Journal of Mathematics, (2019) 16: 88. https://doi.org/10.1007/s00009-019-1365-3
  5. Yampolsky A., Opariy A. Generalized helices in three-dimensional Lie groups, Turkish Journal of Mathematics (2019) 43: 1447 – 1455. http://journals.tubitak.gov.tr/math/
  6. Yampolsky A., Fursenko O. Caustics of wave fronts reflected by a surface, Journal of Mathematical Sciences and Modeling,  2018, V 1 , Issue 2, Pages 131 – 137.  https://doi.org/10.33187/jmsm.431543
  7. Yampolsky A. Eikonal Hypersurfaces in the Euclidean n-Space . Mediterranean Journal of Mathematics, 2017, 14: 160. https://doi.org/10.1007/s00009-017-0965
  8. Yampolsky A. On stability of totally geodesic unit vector fields on three-dimensional Lie groups. Geometry and its Applications. Springer Proceedings in Mathematics & Statistics. -2014. -Vol. 72. -P. 167 –  195
  9. Yampolsky, A. Minimal and Fully Geodesic Cross-Sections of Single-Sphere Bundles. Bulletin of Kharkiv National University, Series: Applied Mathematics and Mechanics, 1030 (2012), 54–70.
  10. Yampolsky A.  On geodesics of tangent bundle with fiberwise deformed Sasaki metric over Kahlerian manifold.   Journal of Math. Phys., Analysis,  Geom.  8/2 (2012),  p. 177 – 189.
  11. Yampolsky A. Totally geodesic vector fields on pseudo-Riemannian manifolds. Bulletin of V.N. Karazin Kharkiv National University, Series: Mathematics, Applied Mathematics, Mechanics.  990 (2011), 4 – 14
  12. Yampolsky A.  Invariant totally geodesic unit vector fields on three-dimensional Lie groups.  Journal of Math. Phys., Analysis,  Geom.  3/2 (2007),  p. 253 – 276.
  13. Yampolsky A. On special types of minimal and totally geodesic unit vector fields. 7-th International Conference on Geometry, Integrability and Quantization, June 2-10, Varna (Bulgaria), SOFTEX, Sofia, 2005, 290 – 304
  14. Yampolsky A. Totally geodesic submanifolds in the tangent bundle of a Riemannian 2-manifold.  Mat. phys., analysis, geometry 2005, 1/1, 116 – 139
  15. Yampolsky A. Totally geodesic unit vector fields on Riemannian  manifold //  Dop. Ukr.  Acad Nauk  2005,  3, 32–35.
  16. Yampolsky A. Full description of totally geodesic unit vector field on Riemannian 2-manifold. Mat. phys., analysis, geometry 2004, 11/3, 355-365.
  17. Yampolsky A., Saharova E. Powers of the space form curvature operator and geodesics of the tangent bundle.  Ukr. Math. Journal  2004, 56/9,  1231-1243.
  18. Yampolsky A. , Abbassi M.T.K. Transverse totally geodesic submanifolds of the tangent bundle. Publ. Math. Debrecen,  64 /1-2 (2004), 129-154
  19. Yampolsky A. On extrinsic geometry of unit normal vector field of Riemannian hyperfoliation. Publ. Math. Debrecen., 63/4 (2003),  555-567.
  20. Yampolsky A. Totally geodesic property of the Hopf vector field. Acta   Math. Hungar.   101, 1-2 (2003), 73-92.
  21. Yampolsky A. On the intrinsic geometry of a unit vector field. Comment.  Math. Univ.  Carolinae 43,  2(2002), 299-317.
  22. Yampolsky A. On the mean curvature of a unit vector field.// Publ. Math. Debrecen, 60(2002), 1/2, 131-155.
  23. Yampolsky A.L. On the vertical strong-sphericity index of Sasaki metric of tangent sphere bundle. Mat. phys., analysis, geometry, 1996, v.3, No 3/4, p. 446-456.
  24. Yampolsky A.L. On the totally geodesic vector fields on submanifold. Mat. phys., analysis, geometry, 1994, v.1,  No 3/4, pp. 540-545.
  1. Yampolsky, O. Analytical Geometry: Theory and Applications. 350 pp. (2026)
  2.  Yampolsky, O. Differential Geometry: A Basic Lecture Course. 350 pp. (2024)
  3.  Yampolsky, O., Shugailo, O. Analytical Geometry: Canonical Curves and Surfaces of the Second Order. V. N. Karazin Kharkiv National University Press, 2021. 100 pp. (ISBN 978-699-285-692-7) 
  4.  Yampolsky, O. Analytical Geometry. Curves and Surfaces of the Second Order: A General Theory. V. N. Karazin Kharkiv National University Press, 2021. 96 pp. (ISBN 978-966-285-691-0) 
  5.  Yampolsky, O. Analytical Geometry: Vectors, Lines, and Planes. V. N. Karazin Kharkiv National University Press, 2020. 116 pp. (ISBN 978-966-285-650-7) (in Ukrainian)

May 2022 – May 2023: University of Waterloo (Canada), visiting researcher.

November 2021 – January 2022: Internship (professional development) at the University of Waterloo (Canada)

May 2018: University of Murcia (Spain), Erasmus+ exchange program

May 2017: University of Murcia (Spain), Erasmus+ exchange program

January–February 2017: University of Waterloo (Canada), internship

January–May 2006: Visiting professor at Texas A&M University (U.S.), teaching the course “Differential Equations Using MAPLE”